College of Liberal Arts and Sciences
Department of Mathematics
Mathematics 120, section E
Calculus and Analytic Geometry, I
1-1:50 PM MWF
314 Altgeld Hall
Professor Daniel R. Grayson
Office: 357 Altgeld Hall
For those of you who are new on campus, welcome to the University and to
college life! You have a straight A average so far at the University of
Illinois, and I will try to help you keep it that way.
For the rest of you, welcome back!
You can succeed in calculus, even though it is harder than the math courses
you have had in high school. It might be twice as hard!
Here is what you have to do.
You should study the book carefully and learn from it outside of class.
It is well written and will reward close study. Plan on allotting at least an
hour per day for this, starting from the first day. We love to answer
questions about the material in the book, so if there is a sentence or
paragraph that doesn't make sense to you, let us know (hopefully, using
the news group) so we can help you out.
The main thing is to start today! At the pace things happen in college, you
don't want to procrastinate for even a week.
Goal of the course:
The chief difference between calculus and high school geometry is
that we take the passage of time into account and use it as a tool.
For example, we might try to measure the volume of a sphere by
letting its radius shrink to zero and recording the rate at which the
The fundamental laws of physics that govern the world tend to be
expressed as differential equations. These equations encapsulate
information about how each little bit of matter interacts with each
other little bit. One of the applications of calculus is to pass
from the fundamental laws to explicit formulas for the global
behavior of particular systems.
In this course we take the first step toward understanding the role
mathematics has to play in coordinating the basic laws of nature by
learning about differentiation and integration of functions.
The textbook is "Calculus: Early Transcendentals", by Stewart, Fourth Edition.
It's available in the book stores.
Lectures take place on Monday, Wednesday, and Friday at 1PM in 314 Altgeld
Hall. In the lectures we will present to you the basic concepts and
tools which you will need for learning the material and attacking the
Discussion sections take place on Tuesday and Thursday at 1 (the R
sections) or 2 PM (the S sections). They have a maximum enrollment of
35, so this is the place where you can get practical help in executing
the algorithms explained in lecture, and you can get answers to your
questions about the material in the book or homework. Prepare for
discussion by reading the material, reviewing your notes from lecture,
and doing the homework.
The discussion leaders will have office hours, mark your homework, grade
your quizzes, and spend time looking at the news group to answer
questions that appear there. You are welcome to go to the office hours
of any of the discussion leaders.
The professor, teaching assistants, and other students will be able to
see the newsgroup, and we will monitor the news group and try to answer
your questions promptly.
If you are using a browser as a newsreader, you will want to tell it
who you are, so the messages you post will be identified. For
example, in Netscape, select "Preferences" from the "Edit" menu, and
then under "Mail & Newsgroups" select "Identity".
Don't be embarrassed about not knowing the answer to a problem. Just
post your question and get the help you need to succeed!
Learn how to post articles to the news group. There are two ways,
depending on whether you want to follow up on a topic in a message
previously posted, or to initiate a new topic of discussion. If
your followups are posted as such, it makes it a lot easier for
readers of the news group to follow the various threads of
Here is a primitive but serviceable way to include mathematical
formulas in email messages and articles in the news group. Use a
caret (^) to indicate exponentiation, an underscore (_) to indicate a
subscript, and an asterisk (*) to indicate multiplication. Thus
"x^2" would mean "x squared", "x_3" would mean "x sub 3", and "x*y"
would mean "x times y". Never use "x" as a "times" sign. Some
formulas can often be rendered in a 2-dimensional form that looks
(x + 2) = x + 4 x + 4
-- = 2x if y = x
If you try that, remember to tell the browser to use a fixed-width
font in that region.
Some of you may also wish to experiment with methods for including
Let's talk about some more detailed ways to access newsgroups from sites
Here's the procedure on PC's.
Here's the procedure for accessing newsgroups from a Macintosh in the
Here is the procedure for getting Outlook Express to look at
My email address is firstname.lastname@example.org. Send me
some introductory email telling me about yourself, once you get the hang of
the email system here. I always reply to email.
If you have a question about a homework problem, I prefer it to be posted to
the news group so my teaching assistants can answer it, and so the other
students can benefit from the answer.
We will cover the following sections of the book: the preview, chapter 1
(except for section 4), chapter 2 (except for section 4), chapter 3,
chapter 4 (except for section 6), chapter 5, chapter 6 (except for
section 3), chapter 8 (section 3 only).
It is important to do the homework so you can learn the material and do
well on the exams, which will draw material substantially from the
Homework is collected every Tuesday and Thursday at the beginning of the
discussion period, and is marked by your discussion leader. It may
happen that more solutions are submitted than can be marked in the time
allotted, in which case we will mark just some of them.
One thing I especially like about the book is the sections called
"Applications Plus" and "Problems Plus". The problems in these sections
demand extra creativity and extra time spent thinking about it. Please
don't get discouraged when you encounter a problem like this and you
don't know the method for solving it immediately. We'll discuss problem
solving techniques in class that ought to apply to this type of problem.
Some students complain that math courses contain tricky problems put
there just to weed out the weaker students, and not for any useful
This is not true. Doing homework problems is a lot like lifting
weights - you have to do it a lot to get strong. We want you to be
strong at solving problems and thinking about mathematics.
Some students complain that there is too much emphasis on theory in
math courses, and that math professors spend too much time explaining
the ideas and not enough time teaching how to execute the algorithms.
If it were possible for you to live in this world and be successful
at your chosen career by following a simple algorithm we would teach
you that algorithm. Life today demands a broad set of adaptible
skills, and a solid intellectual understanding of science and
mathematics is one of them.
Think about those algorithms - do you want to spend all of your time
studying to do something that computers can already do so well? Will
that skill be valuable to your future employer? In real life,
the problems aren't like homework problems. For example, suppose the
problem you confront is to design a way of encoding sound on a CD to
render it more resistant to scratches. Are you going to find the
answer to that in a textbook? Or will you have developed ways of
thinking about problems that will allow you to invent something new
and better than what came before?
There will be frequent quizzes administered in the discussion sections.
Here is the University's academic calendar.
There will be three 1 hour exams in class and a 3 hour final exam, on the
We will use a scoring scheme where 90% or better is an A, 80-90% is
a B, 70-80% is a C, 60-70% is a D, and 0-60% is an F. We will average
your scores so that
If some calamity that may affect your performance befalls you or your
family during the semester, let me know about it right away.
Appeals about scoring:
You are welcome to appeal a score which you think was assigned incorrectly. We
try our best to score correctly.
Office times: Mondays, 2pm, and Wednesdays, 4pm.